Rui De Almeida
Conditional density approximation using fuzzy and probabilistic representations of uncertainty
This presentation will focus on conditional density approximation using fuzzy and probabilistic representations of uncertainty. Fuzzy systems are typically used for approximating deterministic functions, in which case the stochastic uncertainty is ignored. I will present two different systems that combine the fuzzy and probabilistic nature of uncertainty. The obtained semi-parametric models make very few assumptions regarding the functional form of the estimated density or changes across the input variables space. These models possess sufficient generalization power to approximate a non-standard density and ability to describe the underlying process using simple linguistic descriptors despite the complexity and possible non-linearity of these processes. The additional information and process understanding provided by these models are illustrated using a real world example of conditional volatility estimation for the S&P500 index.